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March 12, 2013

Counting and Cardinality in Kindergarten: Meeting the Common Core

By Tiffani Mugurussa
Grades PreK–K

    Have you already switched your teaching focus to Common Core? We’ve been teaching to state and district standards for quite some time, but soon, all states will be teaching to the same standards. I personally like the idea of knowing that when a new student arrives mid-year, I can expect them to be familiar with what I’ve already taught in my own classroom. The Common Core State Standards focus on fewer topics; however, the topics are addressed in greater depth.

    Many standards have been removed from particular grade levels. For example, patterns have always been a huge standard in kindergarten, but are not included in the Common Core State Standards for kindergarten math. By removing some standards CCSS allows teachers to focus on the most important topics in depth, like number sense. By having fewer topics to focus on, students are able to develop a real understanding of a particular topic.

    After reviewing the kindergarten CCSS for math, I felt relief. It wasn’t more topics for me to teach; it was more of what I was already teaching. Instead of spending a few weeks on counting, I can spend a few months working towards 100 percent mastery for all of my students in my classroom. I am no longer tied to a plethora of mathematical topics; instead I am focusing deep and hard on just a few.

    I truly love the kindergarten CCSS for math. Kindergarten is supposed to be a time of learning and growing and developing a love for school. Students need diverse experiences in math such as counting, making sets, and comparing numbers. Their development and understanding of numeracy comes largely through exploration. The Common Core calls for more hands-on opportunities, allowing students to develop and master skills.

     

    K.CC.1 
 Count to 100 by ones and by tens.

    Counting and cardinality is the first domain. It is broken down into seven smaller parts.

    Counting rhymes, books, and puzzles all provide opportunities for students to practice a range of math skills. At the beginning of the school year, we practice counting with several counting rhymes. We also read a variety of counting books. I have several sets of self-checking number puzzles we use during math time.

    These three books represent only a few of our class favorites.

     
    K.CC.2 
 Count forward beginning from a given number within the known sequence (instead of having to begin at 1).

    Once students have an understanding of the count sequence, we start counting on with numbers two through ten. I show students a number on a flash card, and they must tell me what comes next.

    I also have my students play a game I call Counting On. Students take turns with a partner turning over a number card and counting on from the number shown. Once students understand the count sequence and the meaning of what comes next, counting on becomes second nature.

     
    K.CC.3 
 Write numbers from 0 to 20. Represent a number of objects with a written numeral 0–20 (with 0 representing a count of no objects).

    We practice writing numbers daily. The teen numbers can be challenging for some students, especially when we first begin writing numerals. Instead of writing 12, 13, or 14, a few students write 21, 31, or 41. However, most students are capable of writing numbers in sequential order through practice, repetition, and the following activities:

    • Play Dough Number Mats: Students make numbers on the mats with play dough
    • Linker Cube Numbers: Students form numbers out of linker cubes
    • Roll and Write: Roll a number with a die and write it
    • Monthly Calendars: Write the numbers on the calendar

    Count to Tell the Number of Objects

    K.CC.4
  Understand the relationship between numbers and quantities: connect counting to cardinality.
     
    K.CC.5
  Count to answer "how many?" questions about as many as 20 things arranged in a line, a rectangular array, a circle, or as many as 10 things in a scattered configuration; given a number from 1–20, count out that many objects.

    Ten frames are a great way for students to see the numbers and develop subitizing skills. The same is true for dot cards.

     

    Playing games such as concentration with ten frames, dot cards, or even pictures can help students to understand the relationship between numbers and quantities. 

    Each week I introduce a new number to my class. We start with one and work our way to thirty. We build the number on an anchor chart using ten frames, tally marks, a tens and ones chart, and pictures to represent the number. We also use number journals to record the same information. 

    To assess students on number correspondence, we use a sentence strip with random numbers. Students count out the correct number of bears or cubes to match the number. The picture below demonstrates this task.

    Compare Numbers

    K.CC.6
  Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies.

     

    K.CC.7
 Compare two numbers between 1 and 10 presented as written numerals.

    At the beginning of the school year we start out comparing sets of objects. It is easy for a kindergartner to understand the concepts of less and more. As they begin to build an understanding for number concepts we begin to compare numbers less than five before moving to less than ten. We have just recently started working with greater than, less than, and equal to symbols, using the alligator method: the alligator eats the bigger number.

    Websites

    You might find the following websites helpful when looking for ideas on how to teach the Common Core Math Standards:

    http://www.k-5mathteachingresources.com

    http://colaborativelearning.pbworks.com/w/page/31904645/Kindergarten%20Math

    http://www.corestandards.org

    The Common Core State Standards are not only changing the content we teach, but the way we teach it. These new standards are exciting and take us on a journey that I am glad to be a part of from the beginning. Have you begun your journey down the Common Core road? If so, what does the Common Core for math look like in your classroom?

    Have you already switched your teaching focus to Common Core? We’ve been teaching to state and district standards for quite some time, but soon, all states will be teaching to the same standards. I personally like the idea of knowing that when a new student arrives mid-year, I can expect them to be familiar with what I’ve already taught in my own classroom. The Common Core State Standards focus on fewer topics; however, the topics are addressed in greater depth.

    Many standards have been removed from particular grade levels. For example, patterns have always been a huge standard in kindergarten, but are not included in the Common Core State Standards for kindergarten math. By removing some standards CCSS allows teachers to focus on the most important topics in depth, like number sense. By having fewer topics to focus on, students are able to develop a real understanding of a particular topic.

    After reviewing the kindergarten CCSS for math, I felt relief. It wasn’t more topics for me to teach; it was more of what I was already teaching. Instead of spending a few weeks on counting, I can spend a few months working towards 100 percent mastery for all of my students in my classroom. I am no longer tied to a plethora of mathematical topics; instead I am focusing deep and hard on just a few.

    I truly love the kindergarten CCSS for math. Kindergarten is supposed to be a time of learning and growing and developing a love for school. Students need diverse experiences in math such as counting, making sets, and comparing numbers. Their development and understanding of numeracy comes largely through exploration. The Common Core calls for more hands-on opportunities, allowing students to develop and master skills.

     

    K.CC.1 
 Count to 100 by ones and by tens.

    Counting and cardinality is the first domain. It is broken down into seven smaller parts.

    Counting rhymes, books, and puzzles all provide opportunities for students to practice a range of math skills. At the beginning of the school year, we practice counting with several counting rhymes. We also read a variety of counting books. I have several sets of self-checking number puzzles we use during math time.

    These three books represent only a few of our class favorites.

     
    K.CC.2 
 Count forward beginning from a given number within the known sequence (instead of having to begin at 1).

    Once students have an understanding of the count sequence, we start counting on with numbers two through ten. I show students a number on a flash card, and they must tell me what comes next.

    I also have my students play a game I call Counting On. Students take turns with a partner turning over a number card and counting on from the number shown. Once students understand the count sequence and the meaning of what comes next, counting on becomes second nature.

     
    K.CC.3 
 Write numbers from 0 to 20. Represent a number of objects with a written numeral 0–20 (with 0 representing a count of no objects).

    We practice writing numbers daily. The teen numbers can be challenging for some students, especially when we first begin writing numerals. Instead of writing 12, 13, or 14, a few students write 21, 31, or 41. However, most students are capable of writing numbers in sequential order through practice, repetition, and the following activities:

    • Play Dough Number Mats: Students make numbers on the mats with play dough
    • Linker Cube Numbers: Students form numbers out of linker cubes
    • Roll and Write: Roll a number with a die and write it
    • Monthly Calendars: Write the numbers on the calendar

    Count to Tell the Number of Objects

    K.CC.4
  Understand the relationship between numbers and quantities: connect counting to cardinality.
     
    K.CC.5
  Count to answer "how many?" questions about as many as 20 things arranged in a line, a rectangular array, a circle, or as many as 10 things in a scattered configuration; given a number from 1–20, count out that many objects.

    Ten frames are a great way for students to see the numbers and develop subitizing skills. The same is true for dot cards.

     

    Playing games such as concentration with ten frames, dot cards, or even pictures can help students to understand the relationship between numbers and quantities. 

    Each week I introduce a new number to my class. We start with one and work our way to thirty. We build the number on an anchor chart using ten frames, tally marks, a tens and ones chart, and pictures to represent the number. We also use number journals to record the same information. 

    To assess students on number correspondence, we use a sentence strip with random numbers. Students count out the correct number of bears or cubes to match the number. The picture below demonstrates this task.

    Compare Numbers

    K.CC.6
  Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies.

     

    K.CC.7
 Compare two numbers between 1 and 10 presented as written numerals.

    At the beginning of the school year we start out comparing sets of objects. It is easy for a kindergartner to understand the concepts of less and more. As they begin to build an understanding for number concepts we begin to compare numbers less than five before moving to less than ten. We have just recently started working with greater than, less than, and equal to symbols, using the alligator method: the alligator eats the bigger number.

    Websites

    You might find the following websites helpful when looking for ideas on how to teach the Common Core Math Standards:

    http://www.k-5mathteachingresources.com

    http://colaborativelearning.pbworks.com/w/page/31904645/Kindergarten%20Math

    http://www.corestandards.org

    The Common Core State Standards are not only changing the content we teach, but the way we teach it. These new standards are exciting and take us on a journey that I am glad to be a part of from the beginning. Have you begun your journey down the Common Core road? If so, what does the Common Core for math look like in your classroom?

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